A Distributor Has Generated a Rough Estimate of Aftershave Demand $$\begin{array} { l | c c c c } \text { Demand } & 230 & 330 & 430 & 530 \\\hline \text { Weight } & 0.15 & 0.25 & 0.35 & 0.25\end{array}$$

question 41

Essay

A distributor has generated a rough estimate of aftershave demand at their retails store. The distributor is confident that demand will range from 100 to 650. The following table lists weights for demand values within this range.
​ $$\begin{array} { l | c c c c } \text { Demand } & 230 & 330 & 430 & 530 \\\hline \text { Weight } & 0.15 & 0.25 & 0.35 & 0.25\end{array}$$ ​
The distributor pays a wholesale price of $21 per aftershave and then sells at a retail price of $31.
​
a. Construct a spreadsheet model that computes net profit corresponding to a given level of demand and specified order quantity. Model demand as a random variable with ASP's custom general distribution.
b. Using simulation optimization, determine the order quantity that maximizes expected profit. What is the probability of running out of aftershave at this order quantity?
c. How many aftershaves does the distributor need to order so that the probability of running out of aftershaves is only 25 percent? How much expected profit will the distributor lose if he orders this amount rather than the amount from part b?

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Definitions:

SRS

Simple Random Sample, a basic sampling technique in which each member of the population has an equal chance of being included in the sample.

P-value

The probability of observing test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is true.

Statistically Significant

Indicates that the result of a statistical analysis is unlikely to have occurred by chance alone, according to a predefined significance level.

Null Hypothesis

A statement used in statistical testing that assumes no effect or no difference between groups, serving as the default assumption to test against.